Upper bounds for the relaxed area of -valued Sobolev maps and its countably subadditive interior envelope
Giovanni Bellettini
Università di Siena, Siena, Italy; The Abdus Salam International Centre for Theoretical Physics ICTP, Trieste, ItalyRiccardo Scala
Università di Siena, Siena, ItalyGiuseppe Scianna
Università di Siena, Siena, Italy
![Upper bounds for the relaxed area of $\mathbb{S}^{1}$-valued Sobolev maps and its countably subadditive interior envelope cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-rmi.png&w=3840&q=90)
Abstract
Given a connected bounded open Lipschitz set , we show that the relaxed Cartesian area functional of a map is finite, and we provide a useful upper bound for its value. Using this estimate, we prove a modified version of a De Giorgi conjecture adapted to , on the largest countably subadditive set function smaller than or equal to .
Cite this article
Giovanni Bellettini, Riccardo Scala, Giuseppe Scianna, Upper bounds for the relaxed area of -valued Sobolev maps and its countably subadditive interior envelope. Rev. Mat. Iberoam. (2024), published online first
DOI 10.4171/RMI/1475